Question: Simplify the following expression and state the condition under which the simplification is valid. You can assume that $p \neq 0$. $n = \dfrac{8(3p + 4)}{7p} \div \dfrac{6(3p + 4)}{-7} $
Solution: Dividing by an expression is the same as multiplying by its inverse. $n = \dfrac{8(3p + 4)}{7p} \times \dfrac{-7}{6(3p + 4)} $ When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ 8(3p + 4) \times -7 } { 7p \times 6(3p + 4) } $ $ n = \dfrac{-56(3p + 4)}{42p(3p + 4)} $ We can cancel the $3p + 4$ so long as $3p + 4 \neq 0$ Therefore $p \neq -\dfrac{4}{3}$ $n = \dfrac{-56 \cancel{(3p + 4})}{42p \cancel{(3p + 4)}} = -\dfrac{56}{42p} = -\dfrac{4}{3p} $